Problem 26 - Fundamentals of Mathematics

Question

For the following 6 problems, write each expression in words. \(15+(-3)\)

Step-by-Step Solution

Answer

Fifteen plus negative three.

Step 1: Identify the Terms

First, look at the expression given: \(15 + (-3)\). There are two terms involved: 15 and -3. The symbol between the numbers is a plus sign, which needs to be correctly expressed in words.

Step 2: Interpret the Expression

In words, the first number, 15, is read as 'fifteen'. The plus sign is read as 'plus'. The negative number, -3, is read as 'negative three'. You need to ensure that the negative sign is included in the reading of the number.

Step 3: Combine the Interpretation in Words

Combine the terms with their respective symbols interpreted in words to form the full verbal expression: 'fifteen plus negative three'.

Key Concepts

Translating Mathematical Symbols into Words

Understanding how to express mathematical symbols in words is crucial for clearly communicating mathematical ideas. It involves breaking down each part of the mathematical expression into understandable language. For instance, with the example \(15 + (-3)\), each number and symbol holds a specific meaning that is translated into words.

Here’s how you can do it:

• Recognize numbers as their spoken equivalents. In the expression, 15 becomes 'fifteen'.
• The plus sign \(+\) translates directly to the word 'plus'.
• A negative number, such as \(-3\), is expressed as 'negative three'. Ensure you mention the negative sign.

Thus, the whole expression \(15 + (-3)\) translates to 'fifteen plus negative three'. Breaking it down this way makes it easier to understand and communicate.

Negative Numbers

Negative numbers are essential in mathematics to express value below zero. They appear in various contexts such as temperatures below freezing, debts, or even depths below sea level.

A few basics to remember about negative numbers:

• A negative number is expressed with a minus sign (-) in front of it, which distinguishes it from positive numbers.
• When reading or writing negative numbers, always include the word 'negative' in front. For instance, \(-3\) is always said as 'negative three'.

Understanding negative numbers involves recognizing their place on the number line. They exist to the left of zero, in contrast to positive numbers which are on the right.
When adding negative numbers, as seen in \(15 + (-3)\), it can help to think of them in terms of moving left on the number line. This concept helps visualize the decrease in value.

Mathematical Operations

Mathematical operations represent the processes required to calculate different expressions. The fundamental operations include addition, subtraction, multiplication, and division, each with unique symbols and terms.For the expression in question, \(15 + (-3)\), the operation involved is addition. Here’s how it works:

• Addition (\(+\)): Combines two or more numbers into a single sum. It is often referred to as 'plus'.
• When a positive and a negative number are added, as in \(15 + (-3)\), it acts like subtraction, reducing the larger positive value by the magnitude of the negative value.

In the real world, understanding operations helps simplify complex problems, whether balancing a checkbook or combining measurements in a recipe. Each operation defines the way values are combined to yield a result, enriching mathematical literacy and problem-solving skills.